The present disclosure relates generally to digital imaging and computer graphics, and particularly, to rendering vector image data on a display.
Bezier curves are parametric curves that are generally used in computer graphics applications to model smooth curves with a more simplified geometric definition. A Bezier curve may be defined using an equation or function based on the type of the curve and, thus, the number of control points defining a shape of the curve. However, the use of some Bezier curves may not be ideal for some graphics operations. For example, it may be difficult to calculate a relatively accurate distance from a given point in space to a Bezier curve, particularly with respect to a cubic or higher-order Bezier curve, an operation performed in various types of applications, e.g., applications for rendering vector graphics or tracking the movement of a pointer device between different points of a user interface. This is primarily due to the relative complexity of equations defining such Bezier curves. It may be possible to simplify operations involving a Bezier curve further by approximating the Bezier curve with one or more circular arcs, as the equations defining circular arcs are relatively less complex and thus, may require fewer calculations. However, as Bezier curves have varied curvatures that generally do not resemble circular arcs, the approximation of a Bezier curve or curve segment with a circular arc generally produces some degree of error that may need to be estimated, e.g., for purposes of generating more accurate approximations.